Monday, February 8, 2010

The S&P 500 is now nearly as oversold as it was at some of the worst points of the financial crisis. Below is a chart of the S&P 500's trading range using 3 standard deviations above and below the index's 50-day moving average. The index is currently trading right at the bottom of this range, which didn't happen that often during the last bear market. It definitely hasn't been this oversold at any point during the rally. The index is now down 9% from its closing high on January 19th, which is very close to the standard 10% correction.

I'm going to reprint the whole thing because there is talk, with Goldman's stock down, of the company going private. The bit on standard deviations in the markets is toward the bottom:

Goldman held their conference call with the journos and I am sure there will be commentary far more erudite than anything I could muster, so I will focus on just one small piece of the call. MarketBeat's David Gaffen has the link to Deal Journal's live-blog and says:

...David Viniar, CFO of Goldman Sachs, basically suggested that since nobody knew that AIG was a house of cards, nobody had any reason to suspect anything. “AIG was a triple-A rated company, one of the largest and considered one of the most sophisticated in the world,” he said. And in a response to a question on how Goldman allowed its exposure to AIG to get as large as it did, Mr. Viniar describes positions made in 2006 and early 2007 as if it was a different age, a more innocent time, when magical dwarves ruled the land, before the ring of power had been forged.

“It was a very long time ago,” Mr. Viniar says. “AIG at the time was one of the largest, strongest companies in the entire world, and they were very sophisticated, or appeared to be, a very sophisticated counterparty.” The firm later scaled back trades — by the end of 2007, according to Mr. Viniar....

My question is, "If Goldman Sachs were still a partnership, would they have entered into these transactions in the same size?"

The answer, of course, is no.

If partners equity were at risk, there is no way that they would have depended on ratings agencies to ascertain the strength of their counterparty.

Junior partners would be expected to run honey traps on AIG employees.

Lower level employees would hone their dumpster-diving skills.

Whatever it takes to gain competitive intelligence and safeguard the partnership's capital.

Reading Mr. Viniar's words, I am reminded of his statement on market moves in August, 2007:

“We were seeing things that were 25-standard deviation moves, several days in a row”

Several folks, when they finally quit laughing, pointed out how blatently Mr. V was spinning.Most however underestimated how infrequent 25SD events are, the most common guess being once in 100,000 years. Tee hee.In a snappy little eight page paper "How Unlucky is 25 Sigma" we see that at 7 Sigma the odds are:

...The reader will note that as k gets bigger the probabilities of a k-sigma event fallextremely rapidly:• a 3-sigma event is to be expected about every 741 days or about 1 trading dayin every three years;

• a 4-sigma event is to be expected about every 31,560 days or about 1 tradingday in 126 years (!);

• a 5-sigma event is to be expected every 3,483,046 days or about 1 day every13,932 years(!!)

• a 6-sigma event is to be expected every 1,009,976,678 days or about 1 dayevery 4,039,906 years;

• a 7-sigma event is to be expected every 7.76e+11 days – the number of zerodigits is so large that Excel now reports the number of days using scientificnotation, and this number is to be interpreted as 7.76 days with decimal pointpushed back 11 places. This frequency corresponds to 1 day in 3,105,395,365years....

The authors go on to describe the problems involved in computing numbers on the cosmological scales required for 25 standard deviations. A good read, both for the statistically challenged and for pros like Viniar, a very highly paid PR guy, in addition to his CFO duties.